extreme ultraviolet spectroscopy of impulsive phase solar flare footpoints

In Chapter2the basics of atomic emission line spectroscopy are introduced, coveringthe processes driving electron excitation and de-excitation, the formation of Gaussian line profiles, a

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Graham, David Robert (2014) Extreme ultraviolet spectroscopy of

impulsive phase solar flare footpoints PhD thesis

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Extreme Ultraviolet Spectroscopy

of Impulsive Phase Solar Flare

Footpoints

David Robert Graham, M.Sci

Astronomy and Astrophysics GroupSUPA School of Physics and Astronomy

Kelvin BuildingUniversity of GlasgowGlasgow, G12 8QQScotland, U.K

Presented for the degree of

Doctor of Philosophy

The University of Glasgow

September 2013

This thesis is my own composition except where indicated in the text.

No part of this thesis has been submitted elsewhere for any other degree

or qualification

Copyright c

30th September 2013

Four years suddenly does not seem like such a long time, but it certainly would havefelt far longer without the help of many fantastic people First of all I owe a hugethanks to my parents for getting me into this astronomy business so many years agowith a passing trip to Jodrell Bank, and for all of the help and support over the years,even putting up with the odd ‘project’ in the kitchen or on the driveway

A massive thanks to my supervisor Lyndsay Fletcher for the continuous agement, inspiration, and always helping with a question or idea, especially when twohours later it meant running back to the office to frantically scribble down another 20ideas Thanks also to everyone who has helped along the way, especially Iain Hannah,Hugh Hudson, Nic Labrosse, Ryan Milligan, Helen Mason, Giulio Del Zanna, PeterYoung, David Williams, and everyone on the EIS team

encour-I must also thank Scott Mcencour-Intosh for introducing me to the mysterious world ofspectroscopy and Genetic Algorithms, and agreeing to work with me whilst both timesexpecting a baby! And of course Jørgen, Hazel, and everyone at HAO for helping mesurvive in Boulder

Thanks to everyone in the fantastic Glasgow astronomy group, past and present,and everyone who has made a home in Room 604 (and 614!), in particular for real-ising that 4 pm coffee and 6 pm pub are matters of religion, and of course RachaelMcLauchlan for always being able to help with so many last minute travel bookings

I also owe many thanks to the Glasgow University Mountaineering Club, for meetingsome great friends and the countless adventures in the Scottish highlands which havekept me (in)sane Finally, thanks to all my friends and family for reminding me thatthere is a world outside of physics, and for all the support in the form of a walk, pint,

or quick escape down the nearest singletrack

“It was precisely for that reason, to have a bit of a quieter life, that my grandfather came and settled here — Qfwfq said — after the last supernova explosion had flung them once more into space: grandfather, grandmother, their children, grandchildren and great-grandchildren The Sun was just at that stage condensing, a roundish, yel- lowish shape, along one arm of the galaxy, and it made a good impression on him, amidst all the other stars that were going around ‘Let’s try a yellow one this time,’

he said to his wife.”

‘As Long as the Sun Lasts — World Memory and Other Cosmicomic Stories’ (1968)

— by Italo Calvino

for danny

This thesis is primarily concerned with the atmospheric structure of footpoints duringthe impulsive phase of a solar flare Through spectroscopic diagnostics in Extreme-Ultraviolet wavelengths we have made significant progress in understanding the depth

of flare heating within the atmosphere, and the energy transport processes within thefootpoint

Chapter 1 introduces the Sun and its outer atmosphere, forming the necessarybackground to understand the mechanisms behind a solar flare and their observationalcharacteristics The standard flare model is presented which explains the energy sourcebehind a flare, through to the creation of the EUV and X-ray emission

In Chapter2the basics of atomic emission line spectroscopy are introduced, coveringthe processes driving electron excitation and de-excitation, the formation of Gaussian

line profiles, and the formation of density sensitive line ratios The concept of a

differ-ential emission measure is also derived from first principles, followed by a description

of all of the instruments used throughout this thesis

Chapter 3 presents measurements of electron density enhancements in solar flare

footpoints using diagnostics from Hinode/EIS Using RHESSI imaging and spectroscopy,

the density enhancements are found at the location of hard X-ray footpoints and areinterpreted as the heating of layers of increasing depth in the chromosphere to coronaltemperatures

Chapter4shows the first footpoint emission measure distributions (EMD) obtained

from Hinode/EIS data A regularised inversion method was used to obtain the EMD

from emission line intensities The gradient of the EMDs were found to be compatible

with a model where the flare energy input is deposited in an upper layer of the flarechromosphere This top layer then cools by a conductive flux to the denser plasmabelow which then radiates to balance the conductive input The EUV footpoints arefound to be not heated directly by the injected flare energy

In Chapter 5electron densities of over 1013 cm−3 were found using a diagnostic attransition region temperatures It was shown to be difficult to heat plasma at thesedepths with a thick-target flare model and several suggestions are made to explain this;including optical depth effects, non-ionisation equilibrium, and model inaccuracies.Finally, Chapter 6 gathered together both the density diagnostic and EMD results

to attempt to forward fit model atmospheres to observations using a Genetic Algorithm.The results are preliminary, but progress has been made to obtain information about

the T (z) and n(z) profiles of the atmosphere via observation.

1.1 The Sun 2

1.2 The Solar Atmosphere 3

1.3 Solar Flares 8

1.3.1 Observations Characteristics 8

1.3.2 The Standard Flare Model 11

2 Observational Diagnostics and Imaging Spectroscopy 15 2.1 Line Formation 16

2.2 Density Diagnostics 20

2.3 Differential Emission Measure in Temperature 24

2.4 Instrumentation 28

2.4.1 Hinode EIS 28

2.4.2 Hinode XRT 30

2.4.3 Hinode SOT 31

2.4.4 TRACE 31

2.4.5 RHESSI 32

2.4.6 IRIS 33

3 Density and Velocity Measurements of a Solar Flare Footpoint 35 3.1 Flare Observations with Hinode EIS 36

CONTENTS viii

3.1.1 The June 5th 2007 Event 37

3.1.2 GOES and RHESSI 39

3.1.3 TRACE and SOT 40

3.1.4 XRT 44

3.2 Hinode EIS data 46

3.2.1 Data Preparation and Uncertainties 47

3.2.2 Wavelength Calibration 48

3.2.3 Line Analysis 51

3.3 Hinode EIS plasma diagnostics 54

3.3.1 Intensity, Density and Velocities across the region 55

3.3.2 Footpoint Selection 61

3.3.3 High Velocity Flows 61

3.4 Time Evolution of Selected Footpoints 69

3.5 RHESSI data analysis 73

3.6 Processes taking place at the flare footpoints 81

3.6.1 Electron Stopping Depth 83

3.6.2 Electron Beam Power 85

3.6.3 Flow Speeds 86

3.6.4 Electron Beam Heating 87

3.6.5 Thermal Heating 88

3.7 Conclusions 89

4 Impulsive Phase Flare Footpoint Emission Measure Distributions 91 4.1 Secrets of the EMD 93

4.1.1 DEM to EMD 93

4.1.2 EMD Gradients 94

4.1.3 Early Skylab Observations 98

4.2 EIS Data Preparation 100

4.2.1 Line Selection 102

4.2.2 Line Flux 106

CONTENTS ix

4.2.3 Line Blending 108

4.3 Flare Observations and Footpoint Selection 110

4.4 DEM Technique 113

4.4.1 DEM Inputs and Uncertainties 118

4.5 Flare EMDs 120

4.5.1 Measured Footpoint EMD Profiles 122

4.5.2 EMDs for Different Solar Plasmas 123

4.5.3 Examination of the Assumptions Used 126

4.5.4 Varying the Abundance and Ionisation Equilibrium 131

4.5.5 Electron Densities and Emitting Region Thickness 132

4.6 Discussion 135

4.7 Conclusions 139

5 Measurements of High Densities in Flare Footpoints 141 5.1 Oxygen Diagnostics 143

5.2 Fitting 145

5.3 Fitting Results 149

5.4 Footpoint Densities 151

5.5 Interpretation 155

5.5.1 A Collisional Thick Target Approach 158

5.5.2 Testing for Ionisation Equilibrium 161

5.5.3 Electron-Ion Equilibration Time 163

5.5.4 Testing for Optical Depth Effects 165

5.6 Discussion 171

5.7 Conclusion 173

6 Determining Density and Temperature Profiles Through ξ(T ) and ζ(n) 174 6.1 A Differential Emission Measure in Density - Defining the Problem 175

6.2 Finding n(T ) 178

CONTENTS x

6.3 Forward Fitting with PIKAIA - A Genetic Algorithm 179

6.3.1 Trial Models for n(h) and n(T ) 181

6.3.2 Test Event ξ(T ) and Line Intensities 184

6.3.3 Density-Sensitive Emission Lines 184

6.3.4 Contribution Functions 185

6.3.5 The Integral 187

6.3.6 Fitness and Residuals 188

6.4 First Results 188

6.5 Multiple GA Realisations 191

6.6 Conclusions and Future Plans 192

List of Figures

1.1 Temperatures and densities in the solar atmosphere 5

1.2 The chromosphere in Hα 6

1.3 CSHKP flare model 12

1.4 CHIANTI radiative loss curve 13

2.1 Term diagram for Fe xiv 23

2.2 Fe xiv 264/274˚A diagnostic ratio 24

2.3 EIS detector schematic 29

3.1 X-ray light curves for the 5th June 2007 flare 39

3.2 TRACE 171 ˚A for flaring region 42

3.3 TRACE and XRT imaging for the 5th June 2007 flare 43

3.4 Ca ii emission in the northern footpoint 43

3.5 XRT Ti-Poly response and image at second 12-25 keV peak 45

3.6 Intensities, velocities, and densities — Fe xii 57

3.7 Intensities, velocities, and densities — Fe xiii 58

3.8 Intensities, velocities, and densities — Fe xiv 59

3.9 Density diagnostic curves for Fe xii, Fe xiii, and Fe xiv 60

3.10 Footpoint pixels 62

3.11 High temperature velocity shifts at the first 12-25 keV peak 63

3.12 High velocity components in Fe xvi - 15:55:47 UT 64

3.13 High velocity components in Fe xvi - 16:01:05 UT 64

3.14 Double component fits using the R-B asymmetry constraint for Fe xvi 68

LIST OF FIGURES xii

3.15 Time evolution of Position 0 70

3.16 Intensity variation of allowed transition 71

3.17 Time evolution of Position 1 73

3.18 Time evolution of Position 2 73

3.19 RHESSI Imaging and TRACE 74

3.20 RHESSI HXR Spectra 78

3.21 VAL-C and VAL-E stopping column depth for injected electrons 84

4.1 Line contributions varying in temperature, G(T ) 106

4.2 Line contributions varying in density, G(n) 107

4.3 GOES light curves for EMD events 112

4.4 EIS rasters for EMD events 114

4.5 Test EMD solutions for α = 5.0 & α = 5.0 118

4.6 Inverted footpoint EMDs from EIS data 121

4.7 Footpoint, active region, and loop EMD comparison 125

4.8 Inverted footpoint EMDs removing optically thick lines 130

4.9 EMDs varying abundances and ionisation equilibrium 131

5.1 Term diagram for O v 144

5.2 Spectrum of the 192˚A region from CHIANTI v7.1 148

5.3 Fitted spectra for the 192˚A complex 150

5.4 EMDs for both footpoints in Event (a) 152

5.5 Diagnostic curves for ratios found in Table 5.2 153

5.6 O v electron density maps 154

5.7 Hydrogen density, electron density, and temperatures from the VAL-E model 156

5.8 Allred flare model parameters for F10 input 157

5.9 Heating rate per particle in the VAL-E atmosphere 160

5.10 I192/I248 ratios for multiple temperatures 162

5.11 O v 192˚A optical depth 168

LIST OF FIGURES xiii

6.1 Test model atmosphere 182

6.2 G(n) functions for diagnostics lines 187

6.3 First GA forward model results 189

6.4 Residuals for test GA forward model 190

6.5 1000 realisations of the GA fitting 192

Chapter 1

Introduction

People often ask me “Why study the Sun?” It rises every morning, and as far as weknow it will do the same again tomorrow On a good day I can normally think of atleast a handful of reasons why we should be more aware of our parent star Startingfrom the fact its vast output of energy has been the source of heat and light for life tothrive on Earth, to understanding the many aspects of our modern life that are directlyinfluenced by solar activity, such as the communication satellites that guide our mobilephones and Sat Navs, to the national power grids that light our homes, and now,controversially, to the link between solar activity and the extreme winters of recentyears Usually this is met with a nod or a slightly unconvinced acknowledgement Isuppose this is understandable, most of us probably can’t recall the last time a solarflare damaged their iPhone, so it is easy to take for granted something so seeminglyunchanging So for a long time I went without meeting anyone outside of this field whohad first hand experience of solar activity affecting their day-to-day life It seemed Iwould be stuck in trying to convince people that what happens on the Sun can reallyinfluence us here on Earth At least this was the case up until a few weeks ago, aftertalking to an ex-submariner On telling them what I worked on they replied, “oh, solarflares! We had charts to work out how to adjust the radio for them” Apparently,the very low frequency radio waves used to communicate with submarines at shallowdepths are disturbed by changes in the Earth’s ionosphere, a layer which solar flare

1.1: The Sun 2

X-rays easily ionise Being able to predict the disturbance from solar activity thatday is obviously very important to be able to communicate with the crew Of course,this is one of many such examples So whilst it may not be immediately apparent,the Sun has a huge influence on our lives on many scales Even if it simply meansthe GPS takes a little longer to connect one day, or that the lights occasionally flicker

in the house It is therefore crucial to understand what drives phenomena like solarflares as we become more dependent on technology So while we sip on our coffee andcontemplate the latest solar data in the comfort of an air conditioned office, we shouldspare a thought for those worrying about the same, somewhere beneath the sea!

If you are lucky enough to step outside on a clear autumn night, far from any streetlights, houses, and shops, you can marvel at the billions of stars that illuminate thenight sky Their light makes a journey of thousands of light years across our galaxy

to reach us, by which time they are a glittering point in the sky To be visible to usacross such vast distances means they must be immensely bright The power behindthis luminosity is nuclear fusion in the dense core of a star, where hydrogen is fusedtogether releasing energy in the form of radiation

The Sun is one of these billions of stars and is found at centre of our solar system

It is a G-type main sequence star with a surface temperature of around 5800 degreesKelvin Being within such close proximity, the Earth is intimately linked with thephysical processes governing the Sun Over the course of a year parts of the Earthreceive slightly more or less radiation which gives rise to the seasons For us, the dif-ferences between summer and winter are stark, but the change in radiation received

is marginal Should the Sun have been any one of the other classes of star, life wouldhave been very different indeed, if at all possible

The Solar Interior — In the Sun fusion powers a radiating core with a temperature

of around 15 MK and an extremely high electron density of 1034 cm−3 In the core of a

1.2: The Solar Atmosphere 3

solar-like star the opacity is high enough that energetic photons released by fusion arepartially absorbed, keeping the plasma hot enough to maintain fusion, but low enough

to allow energy to eventually escape The energy from fusion is transported by photonswhich interact with the background ions and electrons taking approximately 100,000years to reach the surface However, as the temperature drops towards the exterior ofthe star the opacity increases towards a peak At this point radiation can no longertransport energy efficiently and for the star to remain in hydrostatic equilibrium itmust transport energy by a new means Since the energy transport rate has slowedthe temperature gradient becomes very steep, and at critical gradient, defined by theSchwarzschild criterion, convection will take over from radiative transport Areas with

a plasma density lower than the background will now continue to rise to the surfacemuch like hot air circulating in a heated room Once at the surface the opacity dropsagain and the plasma can radiate into open space and cool before beginning a journeyback towards the inner edge of the convective zone where the cycle is repeated Inhigh resolution imaging the surface of the Sun looks somewhat like a pan of boilingwater Granulation cells of around 1000 km in diameter appear bright in the centre,surrounded by cooler (darker) material that is flowing back towards the core

The solar convective zone is also observed to experience differential rotation, wherethe equatorial regions of the Sun have a rotation period several days faster than at thepoles The effect of this is to create a large shearing of the plasma at the boundary

between the radiative and convective zones known as the tachocline The shearing

motion in this region is now accepted as a possible explanation for the generation oflarge scale solar magnetic fields through a dynamo processes

The Photosphere — The photosphere is often described as the ‘surface’ of the Sun.

As there is no solid surface a definition is often made at the height where the optical

depth becomes less than τ = 1 for wavelengths in the green part of the optical spectrum

at 5000˚A (1˚A = 0.1 nm) The density above the outer edge of the convection zone drops

1.2: The Solar Atmosphere 4

off quickly with height, causing the rate of absorption of photons by negative hydrogenions to also fall Photons emitted from this layer can therefore travel freely into spacewithout being reabsorbed Since the photosphere is significantly brighter than theatmosphere above, it is the layer that we see from Earth The photosphere emits like

an almost perfect black body at a temperature of around 5700 K, radiating around

3.8 × 1026 W of energy into space (Stix 2004) where on average around 1300 Wm−2 ofthis is received at the Earth’s surface

The most prominent observational feature of the photosphere are dark patchesknown as sunspots, which are easily observed by projecting the solar disc onto a whitesurface It is now well established by observation and modelling that sunspots are thelocations of strong magnetic fields of several thousand Gauss originating from below

the photosphere The plasma beta, β = 8πp/B2 where p is the gas pressure and B

is the magnetic field strength, is a ratio of the gas to magnetic pressure in a plasma

Below the photosphere β > 1 and the gas pressure will dictate the motion of the

magnetic field Here convective motions will ‘stir’ the magnetic field, and in places

a collection of magnetic flux tubes may emerge from below the surface and rise into

the solar atmosphere Sunspots appear at the locations of this flux emergence, wherethe magnetic field suppresses the conductive cycle and stops the flow of heat into thephotosphere (Chandrasekhar 1961) The result is that the surface temperature dropswhich appears as a darker area on the solar disc

The Chromosphere — When we talk of the solar atmosphere, we refer to the plasma

between the photosphere and the outer edge of the corona where the tenuous boundarybetween interplanetary space lies At the photosphere the hydrogen density is around

1017 cm−3 but in moving radially outward the density drops rapidly to 109 cm−3 atthe edge of the atmosphere The atmospheric temperature and density as a function

of height has been modelled by Vernazza et al (1981) and we show these parametersfrom their quiet sun model (VAL-C) for reference in Figure 1.1 Due to the lowerdensity the solar atmosphere is much fainter than the photosphere However, thechromosphere can be viewed from Earth by optical instruments using filters at carefully

1.2: The Solar Atmosphere 5

Figure 1.1: Temperature, electron density, and neutral hydrogen density as

functions of height above the photosphere — plotted from parameters modelled

by Vernazza et al (1981)

selected wavelengths that remove the bright contribution from the photosphere Theabsorption lines of Ca ii (singly ionised) H and K lines at 3968˚A and 3933˚A showfeatures close to the temperature minimum at around 500 km The chromosphere canalso be viewed in emission during a total solar eclipse During totality the disc occultsthe photosphere and the chromosphere appears as a red ring around the dark disc

with narrow fiery structures seen extending into space known as spicules The plasma

beta drops in favour of the magnetic field above the photosphere, and this allowsstructures like spicules, extending out to 10,000 km, and cool material trapped inmagnetic loops (prominences) to form The solar atmosphere above the photosphere isvery non-uniform as a result Large scale super-granulation cells are also visible as the

chromospheric network which may be linked by dynamic processes with the corona An

image in H-α of the chromosphere from the Dutch Open Telescope is found in Figure

1.2 showing the chromosphere above a sunspot where dark chromospheric fibrils trace

magnetic structures above the photosphere

In Figure 1.1 we see that the temperature above the photosphere drops slightly to

a minimum around 500 km as would be expected for an atmosphere continuing to lose

1.2: The Solar Atmosphere 6

Figure 1.2: The chromosphere in H-α emission taken by the Dutch Open

Tele-scope Image courtesy of the University of Utrecht and Rob Rutten

energy from radiation and conduction However, the presence of dynamic motions andthe magnetic field (Mariska 1992) increase the temperature again with height Abovethe minimum the temperature rises gradually to around 6000 K at a height of 1000-

2000 km In the model by Gabriel (1976) radiative losses in the hydrogen Lyman-α

line causes another small temperature plateau at around 20,000 K and 2000 km Theregion between 500-2000 km (4000 - 20,000 K) commonly defines the chromosphere

The Transition Region — A description of the transition region is often left to a mere

sentence in many texts, yet it is extremely important in balancing the energy transportbetween the chromosphere and corona The excellent book by John Mariska (Mariska

1992) defines the transition region as the plasma above the temperature plateau at20,000 K and the lower edge of the corona at 106 K The temperature gradient in thisregion is extremely steep and in these models represents a height of only a few km.Emission in this region is dominated by atomic lines such as C iv, O iv, and Si vi

As with the chromosphere, imaging in these lines reveals that the transition region isnot a uniform layer and may be filled with funnels of plasma rising into the coronaand small loops linked to the chromospheric network (Peter 2001) The process that

1.2: The Solar Atmosphere 7

is heating the corona to over 1 MK must transfer its energy through the transitionregion, and in reverse the chromosphere will also be heated through it by conductionfrom hot corona The same is true for any mass that leaves the chromosphere into thesolar wind, or returns back to the solar surface

The Corona — Prior to the invention of the coronagraph, a telescope with an

oc-culting disc in the centre, the corona was only visible during total eclipses as whitediffuse structures extending out into space The hot structures appear white in opticalwavelengths as the emission is predominantly photons from the photosphere scattered

by free electrons in the corona Alongside optical observations the corona is also ble at infrared wavelengths The magnetic field dominates the morphology of the low

visi-density corona The plasma can be described as frozen-in-field as the magnetic field

prevents plasma crossing between field lines Magnetic fields originating from belowthe photosphere trap hot plasma in loops reaching out to around 3 solar radii withtemperatures of 1-3 MK The discovery of the true coronal temperature was an in-teresting test for atomic spectroscopy In the early 1900’s a green emission line wasobserved at 5303˚A which could not be identified as being emitted from any known

element and was assumed to originate from a hypothetical element named coronium.

After some years of improved measurement and atomic theory it was later identified

in the 1930’s to originate from highly ionised iron, which could only be formed at theextreme temperatures in the corona

The processes that gives rise to the extremely high temperatures in the corona havebeen a problem in solar physics for many years One would expect the temperature

to fall off with increasing distance from the photosphere, however, some energy sourcecontinues to heat the corona Various models have be proposed, from the release ofmagnetic energy stored in fields stressed by the motion of the photosphere, plasma waveoscillations leaking from the photosphere and carried into the corona by structures like

spicules, and continuous eruptive events such as nano-flares (Walsh & Ireland 2003;

a large group of sunspots Carrington witnessed extremely bright white spots growing

quickly over the sunspots The Carrington flare was the first recorded example of a

white light flare and is regarded as being the largest flare since geomagnetic eventshave been recorded Flares of this nature are exceptionally rare, although numerousflares of lower energy output may occur daily during periods of high solar activity.The frequency of flares is closely correlated to the solar cycle, a roughly 11 year riseand fall in the number of sunspots As mentioned earlier these sunspots are formed

in regions of strong, complex magnetic fields and plasma in atmosphere above them

is confined and heated by the behaviour of these fields An active region such as this

can be observed from UV up to soft X-Ray and extend high into the corona Duringsolar minimum it is possible to observe almost no sunspots on the disc for days, oreven months in the case of the latest deep 2009-2010 minimum, and flares and eruptiveevents will be rare At solar maximum there can be several large sunspots on the disc

at one time, and their associated active regions will harbour enough energy to releasefrequent flares

A solar flare is a rapid, explosive release of colossal amounts of energy stored in thesolar atmosphere Up to 1033 ergs of magnetic energy can be released in the space of afew minutes to an hour with the cooling of superheated plasma visible for many hoursafter The flare is often accompanied by a readjustment of the coronal magnetic fieldwhich can result in a coronal mass ejection (CME), an eruption of charged particlesinto space, and emission across the entire electromagnetic spectrum from radio bursts

to γ-rays.

Generally, a flare can be characterised by a fast rise in soft X-ray (SXR) flux, the

impulsive phase, followed by a slower decay The total SXR flux between 1-8 ˚A is

1.3: Solar Flares 9

measured by the Geostationary Operational Environmental Satellites (GOES) and isused as a classification for the size of a flare The flare classes start at A for peakfluxes above 10−8 W m−2, B for 10−7 W m−2, and follow the same pattern for C, M,and X class flares X-class flares are rare, with only a handful occurring in a year, butare extremely energetic and are often followed by geomagnetic storms The Halloweenstorms of 2003 were the result of several X-class flares, triggering aurora as far south

as Florida and causing power outages in Sweden

X-rays — The photon spectra of the SXR regime, around 1-10 keV, is primarily the

result of thermal bremsstrahlung radiation emitted by electrons undergoing Coulombcollisions with ions (mostly ionised hydrogen) in a Maxwellian plasma distribution Inthis ‘free-free’ process, the electron is deflected by the ion, loosing a part of its kineticenergy by emitting an X-ray photon The bulk of the flare X-ray emission is emitted bythis thermal process It is mostly emitted by hot plasma which rises and expands into

hot flare loops in the corona, but can sometimes be found in compact areas during the

impulsive phase of the flare (Mrozek & Tomczak 2004) Also important in flare spectraare the high energy bound-bound transitions emitted by ions in high ionisation stateswith filled outer shells such as Fe xvii, Ne IX, and O viii At peak flare temperatures

of 20-30 MK ionisation states as high as Fe xxv are observed Although these arehighly energetic transitions, with photon energies greater than 5 keV, the free-free andfree-bound processes begin to contribute more to the overall emission above 10 MK

In the hard X-ray (HXR) energy range, 10-100 keV, the photon spectra can becharacterised by a high energy power-law tail The primary emission process here isnon-thermal bremsstrahlung, again mostly through electron-ion interactions As withthermal bremsstrahlung, a photon is emitted from an electron loosing energy as it is de-flected However, when the incoming electrons have been accelerated, and are far moreenergetic than the background plasma, the resulting photon spectra deviates from thethermal case and takes the form of a power-law In solar flares, an observed non-thermaltail in the HXR photon spectra is a good indication of the presence of accelerated, or

beamed, electrons In the thin-target approximation, the target density is low, and the

1.3: Solar Flares 10

electron beam is relatively unchanged by the few collisions (suitable in the corona) In

the thick-target case, the ambient density is high such as in the chromosphere The

kinetic energy of the rest ion is relatively unchanged by the bremsstrahlung interaction,and only a very small fraction (∼ 10 −5) of the energy from the fast electron is lost to

bremsstrahlung emission However, in a dense plasma, collisions with other electronsvia Coulomb collisions are much more effective at sharing the kinetic energy due totheir equal mass Most of the beam energy in a thick-target is therefore lost in heatingthe ambient plasma through electron-electron collisions During the flare impulsivephase, HXR emission can often be observed in compact areas deep in chromosphere.These regions are commonly found at the base of flaring loops and are known as the

flare footpoints.

Following the work by Neupert (1968) it was shown that the rate of change of theSXR emission is often similar to the evolution in HXR emission We can arrive atthis conceptually if we consider that the HXR emission is proportional to the poweremitted by the flaring mechanism If we assume that the corona stores this energy,i.e any losses are slow compared to the rate of energy input, then the SXR emissionfound in the corona should be the integral of the HXR emission in time For flareobservations, it is sometimes convenient to estimate the HXR evolution by taking thetime derivative of the SXR emission

Ultraviolet & Extreme-Ultraviolet — We have discussed that the HXR footpoints

could be a location of flare heating through the interaction of non-thermal electronswith the ambient plasma At lower photon energies, Ultraviolet (UV) and Extreme-Ultraviolet (EUV) line emission is also often observed at similar locations to the HXRemission Above the photosphere the higher temperatures and relatively low densitieschange the dominantly observed spectral features from approximately a black-bodywith absorption lines to emission lines and continua The formation temperature ofthese lines ranges from around 10,000 K to over 10 MK In the flare footpoints theyare enhanced significantly with respect to the background transition region and corona.The location of the enhancements varies during the flare evolution, and in the impulsive

1.3: Solar Flares 11

phase UV emission normally associated with the chromosphere is found to be enhanced

in bright ribbons suggesting that the emission originates from low in the solar

atmo-sphere Along these narrow ribbons, brighter compact sources in UV and EUV may

be also found which correspond to the location of the HXR footpoints The bulk ofthe rise phase emission is therefore confined to the lower solar atmosphere As theflare reaches its peak, EUV emission will start to be found in loops extending from theribbon areas into the corona These loops brighten significantly across the flare peakand decay slowly during the gradual phase

Optical — For white light emission to be viewed by projection as easily as the

Car-rington event is exceptional However, optical emission is also observed for a widerange of lower energy flares Even in small events for white light to be viewed againstthe photospheric background requires a large amount of energy, and it is found that alarge part of the total flare emission is in optical and UV wavelengths (Woods et al

2006) The mechanism behind white light emission is still not well understood as itrequires the flare energy deposition to penetrate to below the chromosphere Heatingfrom the chromosphere and proton beams have been suggested as possible solutions

It is generally accepted that the energy source for a flare lies in the coronal magneticfield The emergence of twisted flux from below the photosphere, and motions in thephotosphere can introduce energy into coronal loops which is stored over a period ofhours or even days The system eventually becomes energetically unstable and willrelease the stored energy, either spontaneously or from a perturbation in the field Toproduce the observed heating and non-thermal electron signatures requires a mecha-nism that can release the coronal magnetic energy and raise electrons to non-thermalvelocities In most current flare models, magnetic reconnection is proposed as a solutionthat allows the reconfiguration of the magnetic field to a lower energy state

1.3: Solar Flares 12

Over the past 30 years a relatively consistent picture has emerged for the evolution

of a solar flare The CSHKP model has been widely used as a standard model for solarflares based on the 2D reconnection of a single loop (Carmichael 1964; Sturrock 1966;

layout can be seen in Figure 1.3 The rising plasmoid is a magnetic loop or structurewhich is moving and stretches the field below As the two sides of the loop are drawntogether, the field on the inside of the loop reconnects near the ‘X-point’ (or ‘X-line’ in2.5D), resulting in a new closed loop forming inside the original loop Magnetic energy

is released at or near the X-point region and is directed down the loop field lines intothe footpoints The method of energy transport is still unknown but may take theform of plasma waves or beams of accelerated electrons

The collisional thick-target model (Brown 1971) uses a beam of accelerated electronsinjected from the corona into the chromosphere to generate bremsstrahlung emissionand plasma heating, both of which are routinely observed in HXR and EUV spectra Asecondary effect of the plasma heating is to drive motions in the chromospheric plasma

1.3: Solar Flares 13

If the footpoint plasma is heated beyond the peak of the radiative loss curve (Figure

1.4) then the plasma will not be able to balance the energy input and will begin toexpand, rising back into the loop The process is known as chromospheric evaporation,and is observed by the Doppler shift of hot EUV lines (Doschek et al 1980) and leads

to the hot SXR emission found in flare loops The modelling by Fisher et al (1985)suggests that two types of evaporation exist, gentle and explosive If the heatingtime-scale is less than the local hydrodynamic expansion time-scale (the plasma sound

speed) then the evaporation is gentle The evaporation is considered to be explosive

when the heating time-scale is faster than the plasma can compensate for and the flowspeeds can be above the plasma sound speed The cut-off flare input energy betweenthese scenarios is around 3× 1010 ergs s−1 cm−2

CHIANTI: radiative loss rate

2012) for a density of 1011 cm−3 and coronal abundances.

In the standard flare model the electrons are assumed to be accelerated in theX-point region and precipitate down the magnetic field lines into the chromosphere.This combination of magnetic reconnection and the thick-target model has been thecornerstone of flare research for decades, primarily due to its ability to explain foot-point HXR emission, plasma heating, and chromospheric evaporation However, there

1.3: Solar Flares 14

is still no single agreed method in which the electrons are accelerated in the corona.Problems also exist in transporting charged electrons from the corona to the chromo-sphere without the ‘return current’ that exists to balance the charge and current ofthis beam becoming unstable and halting or significantly redistributing the energy ofthe beam electrons Also, heating deep layers of the atmosphere to create white lightemission is challenging without very high energy electron beams Models involving the

acceleration of electrons locally in the footpoints from the transport of plasma waves

have been proposed to solve these issues (seeRussell & Fletcher (2013))

by the footpoints during a flare is in the form of optically-thin line radiation, which in

UV and EUV wavelengths is rich in diagnostics of temperature, density, and plasmadynamics The goal of this chapter is to present the reader with sufficient background

in the atomic physics leading to these diagnostics, and the necessary assumptions intheir interpretation We begin with an overview of the formation of optically thinemission lines

Observationally, an emission line can be characterised by a Gaussian line profileand is a function of wavelength As the next section will explain, the line emission

is the result of electrons undergoing transitions between states of quantised energies,where photons are emitted at a wavelength inversely proportional to the difference in

energy of the two states (λ0 = hc/(E2 − E1)) For a plasma in thermal equilibrium,the random particle velocities Doppler broaden the emission, resulting in a Gaussian

line profile centred on the rest wavelength λ0 In all fields of astronomy the mostbasic of techniques is to fit a Gaussian profile of three parameters, height, centroidposition, and width, to the observed profile of a spectral line From these three values

2.1: Line Formation 16

we can find the line intensity, velocity of the plasma relative to us, the thermal widthand therefore ion temperature, and if present, estimate the component of non-thermalparticle motions From these relatively simple measurements, astronomers have beenable to learn an enormous amount from incredibly distance sources

Line emission in plasmas and the solar atmosphere is associated with the transitions ofelectrons moving between energy states of an ion or neutral atom A variety of differentphysical processes can initiate these transitions and also lead to ionisation or recom-bination, for example; collisional excitation and de-excitation, spontaneous radiativedecay, or collisional ionisation and dielectronic recombination The characteristic timescale of these depends on the ion density, electron density, and the respective collisioncross sections In the case of a quiet transition region, where the rate of absorption ofbackground photons is low, collisions between ions and free electrons drive the majority

of upward transitions, with radiative decay being responsible for most transitions tolower levels We also note that while in the transition region and corona the spectra isdominated by emission from ions, emission lines from molecules are also found in coolerregions of the Sun Spectral lines from fundamental vibration-rotation transitions of

CO are seen in the µm wavelength range corresponding to temperatures of ∼ 4100 K

or even as low as 3800 K From the work by Avrett (2003) it is apparent that theselines are formed in the temperature minimum at around 500 km above the surface.The balance of ionisation and recombination processes is extremely important inunderstanding the observed line emission The fractional abundance — the proportion

of a plasma in each ionisation stage — depends on this balance between the rate ofelectrons leaving an ion and those recombining The brightness of an emission linefrom an ion then depends on this abundance, therefore, accurate rate calculationsand careful assumptions must be made to ensure that any diagnostics are correct

In most cases the ionisation and recombination time scales are far longer than thecollisional excitation time scales and can be treated separately This is the assumption

2.1: Line Formation 17

of ionisation equilibrium, and the effect of relaxing the assumption in flaring situationswill be discussed throughout this thesis

In the case of the hot, relatively low density, corona and transition region, the

atmosphere can generally be assumed to be optically thin The photons emitted along

the line of sight will therefore travel freely through any material between the sourceand observer At lower temperatures, and higher densities, the plasma can become

optically thick, where the emitted photons may be absorbed, scattered, or re-emitted

before reaching the observer As mentioned, in most circumstances the optically thinassumption is valid, although later in the thesis we have discussed circumstances wherethe assumption may not hold

The final assumption we make before calculating line intensities is to assume thatthe plasma is in local thermal equilibrium Defining the exact temperature of a plasmacan be difficult when the very nature of a plasma lends itself to be influenced bymagnetic fields and ionisation processes, this is especially true in the dynamic solaratmosphere Yet in the regions of the atmosphere we are concerned with, the electron-electron collision times are very short, therefore the plasma will equilibrate quickly totemperature changes We can then assume that the temperature can be described by

a Maxwell-Boltzmann distribution

The emissivity in a transition from an upper level j, to lower level i, emitted by avolume element dV can be expressed as

where A ji is the Einstein coefficient of the transition for spontaneous emission, n j,

the number density of ions in the excited state j, and ν ji is the emitted frequency

In an optically thin plasma the total flux received by an observer is found by

integrating each volume element along the line of the sight, and at a distance R is

2.1: Line Formation 18

Commonly in observational studies this is reduced to an integral over the line ofsight depth; where the spatial resolution of the instrument defines the minimum areathat can be observed

The number density of ions in the excited state n j depends on a combination ofthe excitation processes mentioned above and the plasma temperature and electron

density For many calculations it is easier to express n j as a number of ratios whichcan be individually determined We then have

where n j /n ion is the relative number population of ions in the excited state

com-pared to all other levels, n ion /n el is the abundance of the ionisation stage, n el /n H is

the elemental abundance relative to Hydrogen, and n H /n e is the ratio of the numberdensity of Hydrogen to the electron density

In this thesis we will often refer to these quantities for deriving physical parametersfrom spectra, for example, in density diagnostic ratios, differential emission measures,and finding optical depths We obtain these from various sources The elementalabundances for different parts of the solar atmosphere continue to be measured bymany authors, for example Grevesse & Sauval (1998) and Feldman et al (1992), andare chosen to best suit the solar plasma in question The number density of electronscan be measured spectroscopically or by volume estimates, and the ionisation level inthe atmosphere can be obtained through semi-empirical modelling Theoretical atomicphysics calculations are required for each ion to find the abundance of the ionisationlevel as a function of temperature, for example the percentage of Oxygen v compared to

neutral Oxygen at log T = 5.4 is 54% fromMazzotta et al.(1998) This is also true for

the relative number population n j /n ion, which must be calculated by solving a system

of equations that describe the balance of all excitations and de-excitations for everypossible transition within the ion which is also sensitive to the plasma temperature anddensity

Thanks to a large and ongoing collaborative effort, the CHIANTI atomic physics

2.1: Line Formation 19

database (Dere et al 1997) provides the most up to date calculations and atomic datathat are essential for solar and stellar spectroscopy, for which we are eternally grateful.Compiled from theoretical work and sources such as the National Institute of Standardsand Technology (NIST), it is available for use in the Interactive Data Language (IDL).Results of complex calculations which require many weeks of work are therefore alwaysavailable

Moving back to describing the line emission in terms of the plasma properties, wecan group all of the terms involving the atomic physics of the line formation into a

function of temperature and density called the line contribution function, G(T, n e),where

separating the atomic physics contained in the contribution functions from

infor-mation about the emitting plasma environment The remaining term n2e dV is a

com-bination of the number of free electrons and the electron density n e within a volume

element dv, and is referred to as the emission measure The total emission measure,

2.2: Density Diagnostics 20

function

A very simple temperature diagnostic can be made by studying an image obtained

in one emission line For the majority of strong lines in the EUV range the contributionfunctions are strongly peaked, and an image of the emission around the line centre willreveal bright features emitting at the formation temperature of the line This technique

is the basis of many narrow-band imaging instruments such as TRACE and SDO/AIA.However, the filter bandpass often includes a number of lines at different temperaturescomplicating the analysis, and as we will show later, features in the solar atmosphereare not necessarily isothermal

As was shown towards the end of Section 2.1 the plasma emission measure is tional to the volume of the emitting region and the square of the electron density Asthe depth along the line of sight of a footpoint is hidden to us, the volume can not beexplicitly measured from our instruments, hence the density inferred remains an upper

propor-or lower limit derived from estimates of the emitting region height However, we canamend this through the use of density sensitive line ratios using the excellent spectral

coverage available on instruments such as Hinode/EIS, allowing us to make density

measurements independently of the emitting volume and other plasma properties.Large differences in the spontaneous decay rates of allowed transitions and thosefrom metastable levels lead to varying density sensitivity between emission lines of thesame ion Allowed lines follow the rules for electric dipole transitions and have largetransition probabilities Electrons in metastable levels on the other hand must decay

either via forbidden transitions, a magnetic dipole transition which breaks the L-S coupling selection rules, or intercombination transitions, where the electron moves to

a state with different spin These effects greatly reduce the probability of spontaneousdecays and the emitted flux As the electron density rises, collisional excitation andde-excitation rates will contribute more to the level populations and the flux ratio ofthe two emitted lines becomes sensitive to electron density

2.2: Density Diagnostics 21

Three Level Case — This is best explained through an example of a simple three level

diagnostic A ground state, Level 1, is accompanied by two upper levels where Level 3

is metastable At low densities collisional excitation populates both upper levels andone can assume the two level approximation; where collisional excitations are balanced

by an almost immediate decay from the upper level, and only the ground level andexcited levels are included, i.e no intermediate levels are considered This case where

only the ground level is significantly populated is known as the coronal approximation.

The excitation and de-excitation balance for each transition can be written as

n e n1C12= n2A21, (2.7)

and

n e n1C13= n3A31, (2.8)

where n1, n2, and n3 are the level populations, C12 and C13 the collision excitation

rate coefficients, and A21 and A31 are the decay rates The terms on the left handside give the number of transitions into the excited state while the number of decays

is given on the right — corresponding to the emitted flux in that transition The fluxratio in this case is simply proportional to the ratio of the collision rates, i.e

metastable level since A31 and A32 are small Level 2 will also be de-excited by

colli-sions but the contribution from spontaneous de-excitation A21 is far larger and C21can

be ignored The flux F21 now rises faster than F31 for two reasons More collisional

2.2: Density Diagnostics 22

excitation results in more transitions from Level 2 to 1, but excited electrons in Level

3 may not always spontaneously decay, and collisional de-excitations from Level 3 to 2

will quickly decay, further increasing F21 compared to F31 Eventually the collisionalde-excitation rate in both lines becomes greater than the radiative decays and the flux

ratio returns to approximately the ratio of the spontaneous decay rates A31/A21 Sincethe flux ratio depends on electron density and can be calculated, measurements of theflux in both lines can be used to directly measure the electron density However, un-certainties will arise in the inferred density from errors in obtaining the line flux, such

as blends and fitting errors, and where the assumptions are not suitable for the plasmaconditions

Four Level Case — The density diagnostics used throughout this thesis (see Table

2.1) can all be described by a 4 level system which is common to many EUV diagnostics

in solar and stellar atmospheres This arises from similarities in the ions atomic ture, leading to a pair of transitions sensitive to density, where one of the upper levels

struc-is populated by collstruc-isional excitations from a metastable level The Fe xiv diagnostic

is perhaps the simplest configuration here, arising from the Aluminium isoelectronic

sequence with 3 electrons in the n = 3 outer shell In this case the flux ratio of the λ274

transition, excited from the 3s2 3p2P1/2 ground state, to the λ264 transition, excited

from the 3s2 3p2P3/2 metastable level, is density sensitive A term diagram for the Fexiv diagnostic can be found in Figure2.1

Levels 2, 3, and 4 are all excited via collisions from Level 1 At low densities onlyLevel 1 has a significant population and spontaneous decays from Level 2 to Level 1

are rare due to A21 being very small Of the two allowed lines, the 3 → 1 transition

is brighter than 4 → 2 by around a factor of 2; this is due to the change in angular

momentum required in exciting electrons from the Level 1 2P1/2 state to the Level 4

2P3/2 state - hence C13 C14

As the electron density increases, further collisional excitation boosts the population

in Level 2 as electrons can not easily decay back to Level 1 — this is seen clearly inFigure 2.2 As there is no change in angular momentum between Levels 2 and 4, the

2.2: Density Diagnostics 23

Figure 2.1: Term diagram for Fe xiv showing the four levels involved in the

density diagnostic Level 2 is metastable and has a very low spontaneous decayrate to Level 1 but may be populated at high densities by collisional excitationsfrom Level 1 The red line shows the 264˚A transition which is excited from themetastable state The ratio of this line to the 274˚A transition excited from theground state forms the density diagnostic

collision rate C13 ≈ C24, therefore a second route is available in populating Level 4 and

the ratio F42/F31 rises with density

At very high densities, both the metastable level and ground state populationsbecome balanced by collisional excitation and de-excitation, and flux ratio looses anydensity sensitivity — this is shown on the left of Figure2.2 as the ratio levels off above

1012 cm−3 at a value of 2.9

2.3: Differential Emission Measure in Temperature 24

Figure 2.2: Diagnostic flux ratio for the Fe xiv 264/274 diagnostic In the

left panel the flux ratio is shown across the diagnostic density range On theright panel the electron population in the lower level of the transitions is shown.The population in the metastable level 3s2 3p 2P3/2 can be seen increasing withdensity as collisional excitations fill the level

Many features in the solar atmosphere contain plasma at a range of temperatures, fromlarge scale coronal loops to more compact footpoint sources Even in cases where aplasma may be described as iso-thermal, the temperature distribution is often Gaus-sian in profile Finding the temperature distribution is of great importance for under-standing heating and energy transfer in the solar atmosphere As sources at differenttemperatures in close proximity are never completely isolated when viewed with cur-rent multi-band or spectral imagers, or when viewing optically thin features along theline of sight, we require a method of recovering the temperature distribution within anunresolved volume Finding the differential emission measure (DEM) in temperature is

a technique used extensively throughout solar and astrophysics, returning the ature distribution of the emitting plasma by combining narrowband filter or emissionline intensity measurements sensitive to a range of temperatures

temper-2.3: Differential Emission Measure in Temperature 25

Table 2.1: Density sensitive line pairs used in this thesis The left hand

wave-length in the second column denotes the transition with a metastable lower level

For reference the isoelectronic sequence of the ion is shown and in parenthesis the

lowest similar shell configuration The usable density range is shown in cm−3.

Ion Wavelength (˚A) log Tmax(K) Electron Configuration log n e range

O v 192.904 / 248.460 5.4 Be-like 10.5 - 13.5

Mg vii 280.742 / 278.404 5.8 C-like 8.5 - 11.0

Si x 258.374 / 261.057 6.2 B-like 8.0 - 10.0

Fe xii 186.854+186.887 / 195.120 6.2 P-like (N-like) 9.0 - 11.5

Fe xii 196.640 / 195.120 6.2 P-like (N-like) 9.0 - 11.5

Fe xiii 203.797+203.828 / 202.044 6.2 Si-like (C-like) 8.5 - 10.5

Fe xiv 264.789 / 274.200 6.3 Al-Like (B-like) 9.0 - 11.0

Recovering the DEM from observation is an inverse problem by nature The served intensity is a convolution of the filter or emission lines sensitivity to tempera-ture, and the physical properties of the source itself Given enough sampling across thetemperature range, it is in theory possible to gather information about the source byinversion of the data One of the earliest and most complete definitions of the problem

ob-is found inCraig & Brown (1976) for the application to optically thin X-Ray spectra

We reproduce the derivation here but modified to include the contribution function

G(n, T ) for EUV emission lines.

In the previous section we saw the flux from a given emission line could be described

in terms of the plasma density and contribution function of the line (Equation2.1) If

we define the intensity emitted by the source for an emission line α as

I α =Z

V G(n e (r), T )n2e (r)d3r (2.10)

where n e (r) is the density at position r within a source volume V

The integral over volume can transformed into one in terms of temperature by first